In one type of engine, a NOx catalyst provided on an exhaust passage occludes NOx in exhaust gas when an air-fuel ratio of exhaust gas is in a leaner state than a stoichiometric air-fuel ratio and reduces the occluded NOx when the air-fuel ratio of exhaust gas is in a richer state than the stoichiometric air-fuel ratio. In PATENT DOCUMENT 1, it is disclosed that a NOx reduction control is executed by reducing the air amount and enriching the air-fuel ratio of exhaust gas when the occluded NOx in the NOx catalyst is equal to or greater than a predetermined value.